Physics Help Forum Ranking the Velocity and Acceleration of an Object
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Apr 23rd 2014, 12:39 PM   #3
Junior Member

Join Date: Dec 2012
Posts: 24

Thanks Chip! Perhaps I did not explain the model correctly, then. I guess the velocity is not constant, then. I think I was over-thinking. Basically, the runs are in two segments. Segment 1 from 0 to 10 yards is used to calculate the acceleration rating of a runner while the segment from 10-40 yards is used to calculate his velocity or 'speed' rating.

The way the 'actual' model works is that a runner with a 90 acceleration and 99 speed rating will reach the 40 yard mark at the same time as a runner with an acceleration rating of 99 and speed rating of 90. To me, that means that if you add them up, they will get you the same result. So, if Runner A runs segment 1 in 1.5 seconds and Runner B runs segment 1 in 1.58 seconds, the model states that Runner A is the better 'accelerator' of the two. However, since Runner A runs the final 30 yards in 2.93 seconds compared to Runner B who ran that second segment in 2.85 seconds, we can say that Runner B has a better 'Speed' rating.

The model also dictates that each rating is on a 1-99 scale. So what I am trying to do is determine what each runner's rating for 'Acceleration' and 'Speed' should be so that if you have runners with the same t_t but different t_1 and t_2, they will still reach the 40 yard mark at the same time.

The one thing I neglected was that the first phase is only 25% of the current run, however. So a runner with slow acceleration but faster speed will catch the runner who accelerated quicker but isn't as fast at top speed over the course of the final 30 yards.

Here are the actual u values of the entire population:

u_1 = 1.66
u_2 = 3.15
u_t = 4.81

I tried to use the example I provided with two different runners using your method but I got different results for the segment scores. Can you please walk me through the math to make sure I am doing it correctly to get the scores for Runner A and Runner B? Here are their segment results again.

Runner A:
t_1 = 1.50
t_2 = 2.93
t_t = 4.43

Runner B:
t_1 = 1.58
t_2 = 2.85
t_t = 4.43

I want to state that it DOES make sense that you simply cannnot add them up considering that phase 1 is only 25% of the run. What I really want is a way to accurately predict the ACC and SPD ratings for any runner given their phase 1 and phase 2 segment times so that if they run 40 yards, despite different phase times, they could hypothetically cross the finish line at the 40 yard mark at the same time. Like I said earlier, in the model, a runner with an ACC of 99 and SPD of 90 will cross the 40 yard mark at the same time as a runner with an ACC of 90 and a SPD of 99....in theory.

 Apr 23rd 2014, 02:25 PM #4 Physics Team     Join Date: Jun 2010 Location: Morristown, NJ USA Posts: 2,347 As I said earlier - it's impossible using a linear scale for two runners that have different phase 1 times and phase 2 times but equal total times to also have scores on your 99 point scale add to the same number. Just can't happen, sorry. You must weight the phases according to their value in contributing to the runner's overall result. I suggested that the first phase be rated on a scale of 1-52 and the 2nd phase on a scale of 1-99 -- this would make the math work, but means the max possible score is 99+52=151. Here's how the math works using your data. I found an error in my spreadsheet which I have fixed, so the numbers below are a bit different than in my previous post. There were four runners - the fast runner, the slow runner, and runners A and B. The data is: Phase 1: Fast: 1.4s A: 1.5s B:1.68s Slow:2.19s u_1 = 1.667s Phase 2: Fast: 2.69s A: 2.93s B: 2.85s Slow: 4.24s u_2=3.178s Total: Fast: 4.09s A: 4.43 B: 4.43s Slow:6.43s u_2=4.845s Phase 1 Raw Scores = (u_1-t_1)/u_t Fast: 0.055 A: 0.035 B: 0.018 Slow: -0.108 (Note that the raw scores sum to zero, as expected) Phase 1 Scaled scores on 1-99 scale: Fast: 99 A: 86.5 B: 76.4 Slow: 1 Phase 2 Raw scores = (u_2-t_2)/u_t: Fast: 0.101 A: 0.051 B: 0.068 Slow: -0.219 Phase 2 Scaled scores on 1-99 scale: Fast: 99 A: 83.7 B: 88.8 Slow: 1 Total Raw Scores (u_t-t_t)/u_t: Fast: 0.156 A: 0.086 B: 0.086 Slow: -0.327 Total Scaled score on 1-99 scale: Fast: 99 A: 84.62 B: 84.62 Slow: 1 This gives same total scores to A and B, but note that they are not the simple addition of scores for phases 1 and 2. An alternative: add scaled phase 1 and phase 2 scores, with phase 1 weighted at 52.5%: Fast: 151 A: 129 B: 129 Slow: 1.52 This gives a total score range of 1-151, and perhaps better illustrates that phase 2 results are more important than phase 1. It points out to the runner that improving by 0.1 second in phase 2 is better than improving by 0.1 seconds in phase 1. Hope this helps!
Apr 23rd 2014, 03:57 PM   #5
Junior Member

Join Date: Dec 2012
Posts: 24
Thank you so much again Chip! This definitely helps me identify the flaws I had in my method!

I am also trying to see what method may be best for my analysis. Here is what I am trying to do, so if you have any ideas on the best way to do this, you can get an idea of where I am coming from.

Basically, I have data points for thousands of football players who run 40 yard dashes. This allows scouts to help determine how well a football player accelerates and how fast they move at top speed, given perfect, straight-line, conditions.

The data is measured in seconds and yards with data points at the 10yd, 20yd, and 40yd marks. What I am trying to do is determine how well a player accelerates and how fast they move using this data. It works because the conditions are identical (timing basis and distance) for all players who participate. This allows you to compare one player to another. What I then do is take this data and rate/grade/scale it on a scale of 1 to 99 with 99 being the best and 1 being the worst.

Check out the following video. In this video, both players in the Madden video game run on the field. They both start at the same time and reach the 40 yard mark at the same time.

The bottom player has an ACC rating of 99, evident by his great initial burst where he accelerates away from the top player. The top player has an ACC of 90. However, the top player being to catch and then pull away from the bottom player because his SPD rating is 99 while the bottom player's speed rating is 90. It breaks down like this:

Bottom Player: ACC = 99, SPD = 90.
Top Player: ACC = 90, SPD = 99.

As you can see in the video they both reach the 40 yard mark (at the 50 yard line because they start at the 10 yard line) at the same moment. From this point forward, the acceleration for both players is equal to 0 and the velocity is constant, evident by the Top Player's ability to continue to pull away.

I want to see how I can rate other players with other split times based on this model or something like it. In a previous forum topic, you told me that I have too few data points to create anything of real substance. You recommended that I use the 10yd split time to measure the ACC rating and the 40-10 time to measure the velocity rating.

One thing I considered was finding the average acceleration and velocity for each segment that I have split times for (0-10yds, 10-20yds, and 20-40yds). Then, I can determine the sum of the velocities and accelerations and find the percentage of the total used in each phase. Using that I can try to interpolate an overall ACC and SPD rating.

However, I do not know if this is sound logic or possible. I really need to get down to two numbers that are whole number integers from 1 to 99 for both ACC and SPD.

Would you mind looking at the video and seeing if there is a way that I can attempt to at least mimic how Madden rates the SPD and ACC ratings? Also, can you possibly suggest a way for me to convert real-life 40 yard dash splits into those ratings?

Here is a helpful breakdown of the frames and times for each player in the video to give you an idea of the velocities and accelerations involved for each segment. Keep in mind that I rounded to the nearest .01 and some of the discrepancies are due to the frame counting at each interval which may vary in some instances. You will not that it appears that velocity is constant or close to it from the 40-45 yard segment onward. That means that all acceleration is complete at the 40 yard mark. Most football players are also at peak velocity (acceleration = 0) by the 40 yard mark as well.

Also here are some actual split times of real football players for you to play with. Note that they are all examples from the previous posts.

1.40
2.41
4.24

1.50
2.63
4.43

1.58
2.61
4.43

2.19
3.53
6.17

1.47
2.34
4.16

2.11
3.59
6.33

Thanks again and let me know if you come up with anything useful to help me be as realistic as possible!

DB
Attached Files
 M11 Frames.txt (996 Bytes, 1 views)

Last edited by dcebb2001; Apr 23rd 2014 at 04:01 PM.

 Apr 24th 2014, 07:57 AM #6 Physics Team     Join Date: Jun 2010 Location: Morristown, NJ USA Posts: 2,347 I really have nothing further to add. I think the fact that those two players ended up with the same total rating and that they reached the 40 yard mark at the same time is a fluke. Either that or the weighting is not really from 1-99 for each phase. One thought I had is that if the first phase is actually scored from 48-99 and the second from 1-99 that would make the math work - perhaps that's what they did here. Perhaps a rather extreme example would make this clear. Suppose you had a player who could run at 200 MPH, but at the start he just waits for 4 seconds after the gun goes off, then runs the full 40 yards in 0.43 seconds to have an elapsed time of 4.43 (same as your players A and B previously). This guy would score the absolute worst for the first ten yards, so by your technique gets a score of 1 in the ACC phase, and has the absolute best time for the last 30 yards and so gets SPD =99. Even though he ties players A and B over the full 40 yards he gets a lower total. Player A now has ACC=95 and SPD=34, and player B has ACC=92 and SPD=36.
 Apr 24th 2014, 09:06 AM #7 Junior Member   Join Date: Dec 2012 Posts: 24 Thanks again Chip. That makes sense. I would like to leave the topic open so that anyone with any ideas on a better way I can combat the real overall issue in Post #5 could throw them out there. The big thing I am trying to do: rate players as they are rated in Madden given real data that measures a players acceleration and speed.

 Tags acceleration, object, ranking, velocity